Landau theory of bicriticality in a random quantum rotor system

We consider here a generalization of the random quantum rotor model in which each rotor is characterized by an M-component vector spin. We focus entirely on the case not considered previously, namely when the distribution of exchange interactions has nonzero mean. Inclusion of nonzero mean permits ferromagnetic and superconducting phases for (Formula presented) and (Formula presented) respectively. We find that quite generally, the Landau theory for this system can be recast as a zero-mean problem in the presence of a magnetic field. Naturally then, we find that a Gabay-Toulouse line exists for (Formula presented) when the distribution of exchange interactions has nonzero mean. The solution to the saddle point equations is presented in the vicinity of the bicritical point characterized by the intersection of the ferromagnetic (Formula presented) or superconducting (Formula presented) phase with the paramagnetic and spin glass phases. All transitions including the ferromagnet–spin-glass transition are observed to be second order. At zero temperature, we find that the ferromagnetic order parameter is nonanalytic in the parameter that controls the paramagnet-ferromagnet transition in the absence of disorder. Also for (Formula presented)we find that replica symmetry breaking is present but vanishes at low temperatures. In addition, at finite temperature, we find that the qualitative features of the phase diagram, for (Formula presented) are identical to what is observed experimentally in the random magnetic alloy (Formula presented)